We have proposed a three-dimensional model for the structure of the backbones of thick filaments of the nematode Caenorhabditis elegans, based on electron microscopy and image analysis. In this model, the core is a tubule of seven paramyosin subfilaments, coupled by crosslinking proteins. Thick filament rigidity is a necessary element in the sliding-filament theory of muscle contraction. We have measured the rigidity displayed by these structures in electron micrographs, by the stochastic measure of persistence length. The conventional model of vertebrate thick filaments based solely upon the intertwining of myosin tails in a ropelike manner cannot explain their exceptional flexural rigidity. The coupled tubule principle may explain the rigidity observed in thick filaments and other linear structures